C₁₃×#10124 #15696463

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10124

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#3213	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

492 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21)(16,22,23,29)(17,25,26,20)(19,27,28,24)(30,31,35,38)(32,39,41,44)(33,43,34,37)(36,42,45,40);(17,26)(20,25)(22,29)(24,27)(30,32)(31,36)(33,42)(34,40)(35,41)(37,44)(38,45)(39,43);(14,16)(15,19)(17,27)(18,23)(20,29)(21,28)(22,25)(24,26)(32,40)(33,34)(36,44)(37,43)(39,45)(41,42)

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3112);